# Separability of mixed states: necessary and sufficient conditions

@article{Horodecki1996SeparabilityOM, title={Separability of mixed states: necessary and sufficient conditions}, author={Michal Horodecki and Paweł Horodecki and Ryszard Horodecki}, journal={Physics Letters A}, year={1996}, volume={223}, pages={1-8} }

## 2,101 Citations

Partial separability revisited: Necessary and sufficient criteria

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We extend the classification of mixed states of quantum systems composed of arbitrary numbers of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial…

Separability Properties of Three-mode Gaussian States

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We derive a necessary and sufficient condition for the separability of tripartite three-mode Gaussian states that is easy to check for any such state. We give a classification of the separability…

Separability criteria based on the bloch representation of density matrices

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The necessary condition is proved to be strong enough to detect bound entangled states and the proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them.

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A necessary and sufficient condition for k-separability of pure states in any multipartite quantum systems of finite or infinite dimension is given.

Sufficient and necessary conditions of separability for bipartite pure states in infinite-dimensional systems

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The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable…

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- 1997

Generalized Circulant Densities and a Sufficient Condition for Separability

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- 2008

In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpose (PPT) property can be readily checked. These densities were also…

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